Given two finite sets $A$ and $B$ such that $n(A) = 2$ and $n(B) = 3$. Then the total number of relations from $A$ to $B$ is:

Let $A = \{x, y, z\}$ and $B = \{1, 2\}$. Find the number of relations from $A$ to $B$.

Define a relation $R$ on the set $N$ of natural numbers by $R = \{(x, y) : y = x + 5, x \text{ is a natural number less than } 4; x, y \in N\}$. Depict this relationship using roster form. Write down the domain and the range.

$R$ is a relation from $\{11, 12, 13\}$ to $\{8, 10, 12\}$ defined by $y = x - 3$. Then ${R^{ - 1}}$ is

Let $X = \{ 1, 2, 3, 4, 5 \}$ and $Y = \{ 1, 3, 5, 7, 9 \}$. Which of the following is/are relations from $X$ to $Y$?

If $n(A) = 2$ and the number of relations from set $A$ to set $B$ is $1024$, then $n(B)$ is